8 Supervised -unsupervised semisupervised pattern recognition The major directions of learning are Supervised Patterns whose class is known a-priori are used for training Unsupervised: The number of classes/groups is(in general)unknown and no training patterns are available Semisupervised: a mixed type of patterns is available. For some of them their corresponding class is known and for the rest is not
6 ❖ Supervised – unsupervised – semisupervised pattern recognition: The major directions of learning are: ➢ Supervised: Patterns whose class is known a-priori are used for training. ➢ Unsupervised: The number of classes/groups is (in general) unknown and no training patterns are available. ➢ Semisupervised: A mixed type of patterns is available. For some of them, their corresponding class is known and for the rest is not
CLASSIFTERS BASED ON BAYES DECISION THEORY Statistical nature of feature vectors x=[x,x2…,x丁 8 assign the pattern represented by feature vector x to the most probable of the available classes a122…OM That is x=>@: P(o,lx) maximum
7 CLASSIFIERS BASED ON BAYES DECISION THEORY ❖ Statistical nature of feature vectors ❖ Assign the pattern represented by feature vector to the most probable of the available classes That is maximum T 1 2 l x = x ,x ,...,x x 1 ,2 ,..., M x : P( x) →i i
Computation of a-posteriori probabilities >Assume known a-priori probabilities P(1),P(O2)…P(O4) p(a,),i=1, 2,,M This is also known as the likelihood of xF·toO
8 ❖ Computation of a-posteriori probabilities ➢ Assume known • a-priori probabilities • This is also known as the likelihood of ( ), ( )..., ( ) P 1 P 2 P M p(xi ),i =1,2,...,M . . . i x wr to
The bayes rule(m=2) P(x)P(ox)=p(xo )P(a,)= (@, p(xO)P(O) Where p(x)=∑p(xo)P()
9 = = = = 2 1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) i i i i i i i i i p x p x P p x p x P P x p x P x p x P ➢ The Bayes rule (Μ=2) where
The Bayes classification rule(for two classes M=2) Given x classify it according to the rule P(ax)>P(a2x)x→a fP(a2)>P(a|x)x→O s equivalently: classify x according to the rule P(a)P(a)(<p(xa)P(a) For equiprobable classes the test becomes P(xo(p(xo2
10 ❖ The Bayes classification rule (for two classes M=2) ➢ Given classify it according to the rule ➢ Equivalently: classify according to the rule ➢ For equiprobable classes the test becomes x 2 1 2 1 2 1 ( ) ( ) ( ) ( ) → → P x P x x P x P x x If If ( ) ( )( ) ( ) ( ) 1 1 2 P 2 p x P p x ( )( ) ( ) 1 2 p x p x x